
Program Hamiltonian systems, from topology to applications through analysis
Organizers: Rafael de la Llave (Georgia Institute of Technology), LEAD Albert Fathi (Georgia Institute of Technology; École Normale Supérieure de Lyon), Vadim Kaloshin (University of Maryland), Robert Littlejohn (University of California, Berkeley), Philip Morrison (University of Texas, Austin), Tere Seara (Polytechnical University of Cataluña (Barcelona)), Sergei Tabachnikov (Pennsylvania State University), Amie Wilkinson (University of Chicago)The interdisciplinary nature of Hamiltonian systems is deeply ingrained in its history. Therefore the program will bring together the communities of mathematicians with the community of practitioners, mainly engineers, physicists, and theoretical chemists who use Hamiltonian systems daily. The program will cover not only the mathematical aspects of Hamiltonian systems but also their applications, mainly in space mechanics, physics and chemistry.
The mathematical aspects comprise celestial mechanics, variational methods, relations with PDE, Arnold diffusion and computation. The applications concern celestial mechanics, astrodynamics, motion of satellites, plasma physics, accelerator physics, theoretical chemistry, and atomic physics.
The goal of the program is to bring to the forefront both the theoretical aspects and the applications, by making available for applications the latest theoretical developments, and also by nurturing the theoretical mathematical aspects with new problems that come from concrete problems of applications.
Updated on Aug 20, 2018 08:16 AM PDT 
Program Complementary Program 201819
The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program.
Updated on Jan 02, 2018 10:45 AM PST 
Seminar Hamiltonian Colloquium: Paritytime symmetry entails pseudoHermiticity regardless of diagonalizability
Updated on Dec 04, 2018 12:29 PM PST

Seminar Lunch with Hamilton: Construction of unstable KAM tori for a system of coupled NLS equations.
Updated on Dec 05, 2018 08:59 AM PST 
Program Derived Algebraic Geometry
Organizers: Julie Bergner (University of Virginia), LEAD Bhargav Bhatt (University of Michigan), Dennis Gaitsgory (Harvard University), David Nadler (University of California, Berkeley), Nikita Rozenblyum (University of Chicago), Peter Scholze (Universität Bonn), Gabriele Vezzosi (Università di Firenze)Derived algebraic geometry is an extension of algebraic geometry that provides a convenient framework for directly treating nongeneric geometric situations (such as nontransverse intersections in intersection theory), in lieu of the more traditional perturbative approaches (such as the “moving” lemma). This direct approach, in addition to being conceptually satisfying, has the distinct advantage of preserving the symmetries of the situation, which makes it much more applicable. In particular, in recent years, such techniques have found applications in diverse areas of mathematics, ranging from arithmetic geometry, mathematical physics, geometric representation theory, and homotopy theory. This semester long program will be dedicated to exploring these directions further, and finding new connections.
Updated on Sep 12, 2018 09:26 AM PDT 
Program Birational Geometry and Moduli Spaces
Organizers: Antonella Grassi (University of Pennsylvania), LEAD Christopher Hacon (University of Utah), Sándor Kovács (University of Washington), Mircea Mustaţă (University of Michigan), Martin Olsson (University of California, Berkeley)Birational Geometry and Moduli Spaces are two important areas of Algebraic Geometry that have recently witnessed a flurry of activity and substantial progress on many fundamental open questions. In this program we aim to bring together key researchers in these and related areas to highlight the recent exciting progress and to explore future avenues of research.This program will focus on the following themes: Geometry and Derived Categories, Birational Algebraic Geometry, Moduli Spaces of Stable Varieties, Geometry in Characteristic p>0, and Applications of Algebraic Geometry: Elliptic Fibrations of CalabiYau Varieties in Geometry, Arithmetic and the Physics of String TheoryUpdated on Jan 31, 2017 07:46 PM PST 
Workshop Connections for Women: Derived Algebraic Geometry, Birational Geometry and Moduli Spaces
Organizers: Julie Bergner (University of Virginia), LEAD Antonella Grassi (University of Pennsylvania), Bianca Viray (University of Washington), Kirsten Wickelgren (Georgia Institute of Technology)This workshop will be on different aspects of Algebraic Geometry relating Derived Algebraic Geometry and Birational Geometry. In particular the workshop will focus on connections to other branches of mathematics and open problems. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.
Updated on Oct 17, 2018 08:50 AM PDT 
Seminar Combinatorics Seminar:
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Workshop Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces
Organizers: Julie Bergner (University of Virginia), Bhargav Bhatt (University of Michigan), Christopher Hacon (University of Utah), LEAD Mircea Mustaţă (University of Michigan), Gabriele Vezzosi (Università di Firenze)The workshop will survey several areas of algebraic geometry, providing an introduction to the two main programs hosted by MSRI in Spring 2019. It will consist of 7 expository minicourses and 7 separate lectures, each given by top experts in the field.
The focus of the workshop will be the recent progress in derived algebraic geometry, birational geometry and moduli spaces. The lectures will be aimed at a wide audience including advanced graduate students and postdocs with a background in algebraic geometry.Updated on Dec 07, 2018 09:27 AM PST 
Seminar Combinatorics Seminar:
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Seminar Combinatorics Seminar:
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Seminar Combinatorics Seminar:
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Seminar Combinatorics Seminar:
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Seminar Combinatorics Seminar:
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Seminar Combinatorics Seminar:
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Seminar Combinatorics Seminar:
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Workshop Derived algebraic geometry and its applications
Organizers: Dennis Gaitsgory (Harvard University), David Nadler (University of California, Berkeley), LEAD Nikita Rozenblyum (University of Chicago), Peter Scholze (Universität Bonn), Brooke Shipley (University of Illinois at Chicago)This workshop will bring together researchers at various frontiers, including arithmetic geometry, representation theory, mathematical physics, and homotopy theory, where derived algebraic geometry has had recent impact. The aim will be to explain the ideas and tools behind recent progress and to advertise appealing questions. A focus will be on moduli spaces, for example of principal bundles with decorations as arise in many settings, and their natural structures.
Updated on Sep 06, 2018 04:01 PM PDT 
Seminar Combinatorics Seminar:
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Seminar Combinatorics Seminar:
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Workshop Hot Topics: Recent progress in Langlands Program
Organizers: Mark Kisin (Harvard University), Elena Mantovan (California Institute of Technology), LEAD Xinwen Zhu (California Institute of Technology)The purpose of the workshop is to explain Vincent Lafforgue's ground breaking work, constructing the automorphic to Galois direction of the Langlands correspondence for function fields. There will also be a number of talks on more recent developments and related results.
Updated on Sep 06, 2018 04:11 PM PDT 
Seminar Combinatorics Seminar:
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Seminar Combinatorics Seminar:
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Seminar Combinatorics Seminar:
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Seminar Combinatorics Seminar:
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Workshop Recent Progress in Moduli Theory
Organizers: Lucia Caporaso (University of Rome, Roma 3), LEAD Sándor Kovács (University of Washington), Martin Olsson (University of California, Berkeley)This workshop will be focused on presenting the latest developments in moduli theory, including (but not restricted to) recent advances in compactifications of moduli spaces of higher dimensional varieties, the birational geometry of moduli spaces, abstract methods including stacks, stability criteria, and applications in other disciplines.Updated on Sep 06, 2018 04:06 PM PDT 
Summer Graduate School Commutative Algebra and its Interaction with Algebraic Geometry
Organizers: Craig Huneke (University of Virginia), Sonja Mapes (University of Notre Dame), Juan Migliore (University of Notre Dame), LEAD Claudia Polini (University of Notre Dame), Claudiu Raicu (University of Notre Dame)Linkage is a method for classifying ideals in local rings. Residual intersections is a generalization of linkage to the case where the two `linked' ideals need not have the same codimension. Residual intersections are ubiquitous: they play an important role in the study of blowups, branch and multiple point loci, secant varieties, and Gauss images; they appear naturally in intersection theory; and they have close connections with integral closures of ideals.
Commutative algebraists have long used the Frobenius or pth power map to study commutative rings containing a finite field. The theory of tight closure and test ideals has widespread applications to the study of symbolic powers and to BrianconSkoda type theorems for equicharacteristic rings.
Numerical conditions for the integral dependence of ideals and modules have a wealth of applications, not the least of which is in equisingularity theory. There is a long history of generalized criteria for integral dependence of ideals and modules based on variants of the HilbertSamuel and the BuchsbaumRim multiplicity that still require some remnants of finite length assumptions.
The Rees ring and the special fiber ring of an ideal arise in the process of blowing up a variety along a subvariety. Rees rings and special fiber rings also describe, respectively, the graphs and the images of rational maps between projective spaces. A difficult open problem in commutative algebra, algebraic geometry, elimination theory, and geometric modeling is to determine explicitly the equations defining graphs and images of rational maps.
The school will consist of the following four courses with exercise sessions plus a Macaulay2 workshop
 Linkage and residual intersections
 Characteristic p methods and applications
 Blowup algebras
 Multiplicity theory
Updated on Aug 09, 2018 12:27 PM PDT 
Summer Graduate School Random and arithmetic structures in topology
Organizers: LEAD Alex Furman (University of Illinois at Chicago), Tsachik Gelander (Weizmann Institute of Science)The study of locally symmetric manifolds, such as closed hyperbolic manifolds, involves geometry of the corresponding symmetric space, topology of towers of its finite covers, and numbertheoretic aspects that are relevant to possible constructions.The workshop will provide an introduction to these and closely related topics such as lattices, invariant random subgroups, and homological methods.Updated on Apr 20, 2018 03:02 PM PDT 
MSRIUP MSRIUP 2019: Combinatorics and Discrete Mathematics
Organizers: Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Franco (Queensborough Community College (CUNY); MSRI  Mathematical Sciences Research Institute), LEAD Rebecca Garcia (Sam Houston State University), Pamela Harris (Williams College), Suzanne Weekes (Worcester Polytechnic Institute)The MSRIUP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.
In 2019, MSRIUp will focus on the application of combinatorial arguments and techniques to enumerate, examine, and investigate the existence of discrete mathematical structures with certain properties. The areas of interest for these applications encompass a wide range of mathematical fields and will include algebra, number theory, and graph theory, through weight multiplicity computations, the study of vector partition functions, and graph domination problems, respectively. The research program will be led by Dr. Pamela E. Harris, Assistant Professor of Mathematics at Williams College.
Updated on Nov 21, 2018 11:48 AM PST 
Summer Graduate School Representation stability
Organizers: Thomas Church (Stanford University), LEAD Andrew Snowden (University of Michigan), Jenny Wilson (Stanford University)This summer school will give an introduction to representation stability, the study of algebraic structural properties and stability phenomena exhibited by sequences of representations of finite or classical groups  including sequences arising in connection to hyperplane arrangements, configuration spaces, mapping class groups, arithmetic groups, classical representation theory, Deligne categories, and twisted commutative algebras. Representation stability incorporates tools from commutative algebra, category theory, representation theory, algebraic combinatorics, algebraic geometry, and algebraic topology. This workshop will assume minimal prerequisites, and students in varied disciplines are encouraged to apply.
Updated on Aug 03, 2018 11:17 AM PDT 
Summer Graduate School Séminaire de Mathématiques Supérieures 2019: Current trends in Symplectic Topology
Organizers: Octav Cornea (Université de Montréal), Yakov Eliashberg (Stanford University), Michael Hutchings (University of California, Berkeley), Egor Shelukhin (Université de Montréal)Symplectic topology is a fast developing branch of geometry that has seen phenomenal growth in the last twenty years. This two weeks long summer school, organized in the setting of the Séminaire de Mathématiques Supérieures, intends to survey some of the key directions of development in the subject today thus covering: advances in homological mirror symmetry; applications to hamiltonian dynamics; persistent homology phenomena; implications of flexibility and the dichotomy flexibility/rigidity; legendrian contact homology; embedded contact homology and fourdimensional holomorphic techniques and others. With the collaboration of many of the top researchers in the field today, the school intends to serve as an introduction and guideline to students and young researchers who are interested in accessing this diverse subject.
Updated on Dec 10, 2018 04:21 PM PST 
Summer Graduate School Geometric Group Theory
Organizers: LEAD Rita Jiménez Rolland (Instituto de Matematicás, UNAMOaxaca), LEAD Pierre Py (Instituto de Matematicás, UNAMCiudad Universitaria)Geometric group theory studies discrete groups by understanding the connections between algebraic properties of these groups and topological and geometric properties of the spaces on which they act. The aim of this summer school is to introduce graduate students to specific central topics and recent developments in geometric group theory. The school will also include students presentations to give the participants an opportunity to practice their speaking skills in mathematics. Finally, we hope that this meeting will help connect Latin American students with their American and Canadian counterparts in an environment that encourages discussion and collaboration.
Updated on Aug 06, 2018 11:13 AM PDT 
Summer Graduate School Polynomial Method
Organizers: Adam Sheffer (Bernard M. Baruch College, CUNY), LEAD Joshua Zahl (University of British Columbia)In the past eight years, a number of longstanding open problems in combinatorics were resolved using a new set of algebraic techniques. In this summer school, we will discuss these new techniques as well as some exciting recent developments.
Updated on Nov 06, 2018 10:39 AM PST 
Summer Graduate School Recent topics on wellposedness and stability of incompressible fluid and related topics
Organizers: LEAD Yoshikazu Giga (University of Tokyo), Maria Schonbek (University of California, Santa Cruz), Tsuyoshi Yoneda (University of Tokyo)The purpose of the workshop is to introduce graduate students to fundamental results on the NavierStokes and the Euler equations, with special emphasis on the solvability of its initial value problem with rough initial data as well as the large time behavior of a solution. These topics have long research history. However, recent studies clarify the problems from a broad point of view, not only from analysis but also from detailed studies of orbit of the flow.
Updated on Jul 31, 2018 11:48 AM PDT 
Summer Graduate School Toric Varieties
Organizers: David Cox (Amherst College), Henry Schenck (Iowa State University)Toric varieties are algebraic varieties defined by combinatorial data, and there is a wonderful interplay between algebra, combinatorics and geometry involved in their study. Many of the key concepts of abstract algebraic geometry (for example, constructing a variety by gluing affine pieces) have very concrete interpretations in the toric case, making toric varieties an ideal tool for introducing students to abstruse concepts.
Updated on Sep 21, 2018 04:02 PM PDT 
Summer Graduate School HPrinciple
Organizers: LEAD Emmy Murphy (Northwestern University), Takashi Tsuboi (University of Tokyo)This two week summer school will introduce graduate students to the theory of hprinciples. After building up the theory from basic smooth topology, we will focus on more recent developments of the theory, particularly applications to symplectic and contact geometry, fluid dynamics, and foliation theory.
Updated on Sep 21, 2018 04:02 PM PDT 
Summer Graduate School Mathematics of Machine Learning
Organizers: Sebastien Bubeck (Microsoft Research), Anna Karlin (University of Washington), Adith Swaminathan (Microsoft Research)Learning theory is a rich field at the intersection of statistics, probability, computer science, and optimization. Over the last decades the statistical learning approach has been successfully applied to many problems of great interest, such as bioinformatics, computer vision, speech processing, robotics, and information retrieval. These impressive successes relied crucially on the mathematical foundation of statistical learning.
Recently, deep neural networks have demonstrated stunning empirical results across many applications like vision, natural language processing, and reinforcement learning. The field is now booming with new mathematical problems, and in particular, the challenge of providing theoretical foundations for deep learning techniques is still largely open. On the other hand, learning theory already has a rich history, with many beautiful connections to various areas of mathematics (e.g., probability theory, high dimensional geometry, game theory). The purpose of the summer school is to introduce graduate students (and advanced undergraduates) to these foundational results, as well as to expose them to the new and exciting modern challenges that arise in deep learning and reinforcement learning.
Updated on Nov 30, 2018 06:41 PM PST 
Program Holomorphic Differentials in Mathematics and Physics
Organizers: LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at UrbanaChampaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas, Austin), Anna Wienhard (RuprechtKarlsUniversität Heidelberg), Anton Zorich (Institut de Mathematiques de Jussieu)Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukayatype categories, links to quantum integrable systems, or the physically derived construction of socalled spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special  Hitchin or higher Teichmuller  components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).
It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our program will be of interest to those working in many different elds, including lowdimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).
Updated on Apr 10, 2018 10:50 AM PDT 
Program Microlocal Analysis
Organizers: Pierre Albin (University of Illinois at UrbanaChampaign), Nalini Anantharaman (Université de Strasbourg), Kiril Datchev (Purdue University), Raluca Felea (Rochester Institute of Technology), Colin Guillarmou (Université de Paris XI (ParisSud)), LEAD Andras Vasy (Stanford University)Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory… This program will bring together researchers from various parts of the field to facilitate the transfer of ideas, and will also provide a comprehensive introduction to the field for postdocs and graduate students.
Updated on Apr 13, 2018 11:42 AM PDT 
Program Complementary Program 201920
The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program.
Updated on Nov 27, 2018 12:28 PM PST 
Workshop Connections for Women: Holomorphic Differentials in Mathematics and Physics
Organizers: Laura Fredrickson (Stanford University), Lotte Hollands (HeriotWatt University, Riccarton Campus), LEAD Qiongling Li (Chern Institute of Mathematics), Anna Wienhard (RuprechtKarlsUniversität Heidelberg), Grace Work (University of Illinois at UrbanaChampaign)This twoday workshop will consist of various talks given by prominent female mathematicians on topics of new developments in the role of holomorphic differentials on Riemann surfaces. These will be appropriate for graduate students, postdocs, and researchers in areas related to the program.
This workshop is open to all mathematicians.Updated on May 10, 2018 09:01 AM PDT 
Workshop Introductory Workshop: Holomorphic Differentials in Mathematics and Physics
Organizers: LEAD Jayadev Athreya (University of Washington), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas, Austin), Anna Wienhard (RuprechtKarlsUniversität Heidelberg)Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In this introductory workshop, we will bring junior and senior researchers from this diverse range of subjects together in order to explore common themes and unexpected connections.
Updated on Nov 21, 2017 04:24 PM PST 
Workshop Connections for Women: Microlocal Analysis
Organizers: Tanya Christiansen (University of Missouri), LEAD Raluca Felea (Rochester Institute of Technology)This workshop will provide a gentle introduction to a selection of applications of microlocal analysis. These may be drawn from among geometric microlocal analysis, inverse problems, scattering theory, hyperbolic dynamical systems, quantum chaos and relativity. The workshop will also provide a panel discussion, a poster session and an introduction/research session.
This workshop is open to all mathematicians.
Updated on Oct 22, 2018 11:23 AM PDT 
Workshop Introductory Workshop: Microlocal Analysis
Organizers: Pierre Albin (University of Illinois at UrbanaChampaign), LEAD Raluca Felea (Rochester Institute of Technology), Andras Vasy (Stanford University)Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory… This workshop will provide a comprehensive introduction to the field for postdocs and graduate students as well as specialists outside the field, building up from standard facts about the Fourier transform, distributions and basic functional analysis.
Updated on Sep 24, 2018 01:43 PM PDT 
Workshop Recent developments in microlocal analysis
Organizers: LEAD Pierre Albin (University of Illinois at UrbanaChampaign), Nalini Anantharaman (Université de Strasbourg), Colin Guillarmou (Université de Paris XI (ParisSud))Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory, hyperbolic dynamical systems, probability… As this description shows microlocal analysis has become a very broad area. Due to its breadth, it is a challenge for researchers to be aware of what is happening in other parts of the field, and the impact this may have in their own research area. The purpose of this workshop is thus to bring together researchers from different parts of microlocal analysis and its applications to facilitate the transfer of new ideas.
Updated on May 08, 2018 03:21 PM PDT 
Workshop Holomorphic Differentials in Mathematics and Physics
Organizers: LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at UrbanaChampaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas, Austin), Anton Zorich (Institut de Mathematiques de Jussieu)Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukayatype categories, links to quantum integrable systems, or the physically derived construction of socalled spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special  Hitchin or higher Teichmuller  components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).
It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our workshop will be of interest to those working in many different fields, including lowdimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).
Updated on May 14, 2018 02:00 PM PDT 
Program Quantum Symmetries
Organizers: Vaughan Jones (Vanderbilt University), LEAD Scott Morrison (Australian National University), Victor Ostrik (University of Oregon), Emily Peters (Loyola University), Eric Rowell (Texas A & M University), LEAD Noah Snyder (Indiana University), Chelsea Walton (University of Illinois at UrbanaChampaign)Symmetry, as formalized by group theory, is ubiquitous across mathematics and science. Classical examples include point groups in crystallography, Noether's theorem relating differentiable symmetries and conserved quantities, and the classification of fundamental particles according to irreducible representations of the Poincaré group and the internal symmetry groups of the standard model. However, in some quantum settings, the notion of a group is no longer enough to capture all symmetries. Important motivating examples include Galoislike symmetries of von Neumann algebras, anyonic particles in condensed matter physics, and deformations of universal enveloping algebras. The language of tensor categories provides a unified framework to discuss these notions of quantum symmetry.Updated on Mar 22, 2018 11:21 AM PDT 
Program Higher Categories and Categorification
Organizers: David Ayala (Montana State University), Clark Barwick (University of Edinburgh), David Nadler (University of California, Berkeley), LEAD Emily Riehl (Johns Hopkins University), Marcy Robertson (University of Melbourne), Peter Teichner (MaxPlanckInstitut für Mathematik), Dominic Verity (Macquarie University)Though many of the ideas in higher category theory find their origins in homotopy theory — for instance as expressed by Grothendieck’s “homotopy hypothesis” — the subject today interacts with a broad spectrum of areas of mathematical research. Unforeseen descent, or localtoglobal formulas, for familiar objects can be articulated in terms of higher invertible morphisms. Compatible associative deformations of a sequence of maps of spaces, or derived schemes, can putatively be represented by higher categories, as Koszul duality for E_nalgebras suggests. Higher categories offer unforeseen characterizing universal properties for familiar constructions such as Ktheory. Manifold theory is natively connected to higher category theory and adjunction data, a connection that is most famously articulated by the recently proven Cobordism Hypothesis.
In parallel, the idea of "categorification'' is playing an increasing role in algebraic geometry, representation theory, mathematical physics, and manifold theory, and higher categorical structures also appear in the very foundations of mathematics in the form of univalent foundations and homotopy type theory. A central mission of this semester will be to mitigate the exorbitantly high "cost of admission'' for mathematicians in other areas of research who aim to apply higher categorical technology and to create opportunities for potent collaborations between mathematicians from these different fields and experts from within higher category theory.Updated on Oct 05, 2018 12:21 PM PDT 
Workshop Connections for Women: Quantum Symmetries
Organizers: Emily Peters (Loyola University), LEAD Chelsea Walton (University of Illinois at UrbanaChampaign)This workshop will feature several talks by experts, along with numerous 5minute presentations by junior mathematicians, on topics related to Quantum Symmetry. Such topics will include tensor categories, subfactors, Hopf algebras, topological quantum field theory and more. There will also be a panel discussion on professional development. The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.
Updated on Mar 26, 2018 12:18 PM PDT 
Workshop Introductory Workshop: Quantum Symmetries
Organizers: Vaughan Jones (Vanderbilt University), Victor Ostrik (University of Oregon), Emily Peters (Loyola University), LEAD Noah Snyder (Indiana University)This workshop will consist of introductory minicourses on key topics in Quantum Symmetry: fusion categories, modular tensor categories, Hopf algebras, subfactors and planar algebras, topological field theories, conformal nets, and topological phases of matter. These minicourses will be introductory and are aimed at giving semester participants exposure to the main ideas of subfields other than their own.
Updated on Apr 09, 2018 02:20 PM PDT 
Workshop Connections for Women: Higher Categories and Categorification
Organizers: Emily Riehl (Johns Hopkins University), LEAD Marcy Robertson (University of Melbourne)This twoday workshop will survey notable developments in the foundations and applications of higher category theory. It will consist of two minicourses given by emerging female leaders in the subject: Claudia Scheimbauer and Nathalie Wahl. This will be paired with a problem sessions lead by selected "TA's", themselves experts in higher structures. Each lecture series will be tailored to a diverse audience, accessible to graduate students and nonexpert researchers with some background in homological algebra.
The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.
Updated on Sep 14, 2018 02:07 PM PDT 
Workshop Introductory Workshop: Higher Categories and Categorification
Organizers: LEAD David Ayala (Montana State University), Emily Riehl (Johns Hopkins University), Christopher SchommerPries (University of Notre Dame), Peter Teichner (MaxPlanckInstitut für Mathematik)This workshop will survey notable developments and applications of higher category theory; it will be a venue for endusers to share their vision of how to apply the theory, as well as developers to share technical advancements. It will consist of 6 series of 3 lectures, each given by instrumental endusers & developers of higher category theory, together with a few questionanswer sessions. Each lecture series will be tailored to a diverse audience, accessible to graduate students and nonexpert researchers with some background in homological also algebra. The content of these lecture series will concern the following topics.
 Ktheory: categorification, noncommutative motives, trace methods;
 TQFT: functorial field theories, factorization homology.
 Parametrized higher category theory: stratifications, equivariant homotopy theory, operads, deformation theory and Koszul duality.
 Synthetic higher category theory: modelindependent characterizations, cosmoi.
Updated on Sep 14, 2018 02:08 PM PDT 
Workshop Tensor categories and topological quantum field theories
Organizers: Scott Morrison (Australian National University), Eric Rowell (Texas A & M University), LEAD Claudia Scheimbauer (Norwegian University of Science and Technology (NTNU)), Christopher SchommerPries (University of Notre Dame)The workshop will concern the latest developments in the mathematical study of quantum field theories. The focus will be on the interplay among topics such as higher category theory, as illustrated by the cobordism hypothesis, conformal field theory, tensor categories describing the quantum symmetries, and the relation to topological phases of matter.
Updated on Jul 03, 2018 04:02 PM PDT 
Workshop (∞, n)categories,factorization homology, and algebraic Ktheory
Organizers: LEAD Clark Barwick (University of Edinburgh), David Gepner (University of Melbourne), David Nadler (University of California, Berkeley), Marcy Robertson (University of Melbourne)This workshop will focus on recent developments in factorization homology, parametrized homotopy theory, and algebraic Ktheory. These seemingly disparate topics are unified by a common methodology, which leverages universal properties and unforeseen descent by way of higher category theory. Furthermore, they enjoy powerful and complementary roles in application to the cyclotomic trace. This workshop will be a venue for experts in these areas to present new results, make substantive connections across fields, and suggest and contextualize outstanding questions and problems. It will consist of 9 speakers, each delivering a 1hour morning talk and a 1hour afternoon talk, in addition to a session reserved for drawing attention to an assortment of outstanding problems.
Updated on Jun 25, 2018 10:56 AM PDT 
Program Random and Arithmetic Structures in Topology
Organizers: Nicolas Bergeron (Université de Paris VI (Pierre et Marie Curie)), Jeffrey Brock (Brown University), Alex Furman (University of Illinois at Chicago), Tsachik Gelander (Weizmann Institute of Science), Ursula Hamenstädt (Rheinische FriedrichWilhelmsUniversität Bonn), Fanny Kassel (Institut des Hautes Études Scientifiques (IHES)), LEAD Alan Reid (Rice University)The use of dynamical invariants has long been a staple of geometry and topology, from rigidity theorems, to classification theorems, to the general study of lattices and of the mapping class group. More recently, random structures in topology and notions of probabilistic geometric convergence have played a critical role in testing the robustness of conjectures in the arithmetic setting. The program will focus on invariants in topology, geometry, and the dynamics of group actions linked to random constructions.
Updated on Nov 16, 2017 02:50 PM PST 
Program Decidability, definability and computability in number theory
Organizers: Valentina Harizanov (George Washington University), Moshe Jarden (TelAviv University), Maryanthe Malliaris (University of Chicago), Barry Mazur (Harvard University), Russell Miller (Queens College, CUNY), Jonathan Pila (University of Oxford), LEAD Thomas Scanlon (University of California, Berkeley), Alexandra Shlapentokh (East Carolina University), Carlos Videla (Mount Royal University)This program is focused on the twoway interaction of logical ideas and techniques, such as definability from model theory and decidability from computability theory, with fundamental problems in number theory. These include analogues of Hilbert's tenth problem, isolating properties of fields of algebraic numbers which relate to undecidability, decision problems around linear recurrence and algebraic differential equations, the relation of transcendence results and conjectures to decidability and decision problems, and some problems in anabelian geometry and field arithmetic. We are interested in this specific interface across a range of problems and so intend to build a semester which is both more topically focused and more mathematically broad than a typical MSRI program.
Updated on Oct 05, 2018 09:07 AM PDT 
Workshop Connections for Women: Random and Arithmetic Structures in Topology
Organizers: LEAD Ursula Hamenstädt (Rheinische FriedrichWilhelmsUniversität Bonn), LEAD Fanny Kassel (Institut des Hautes Études Scientifiques (IHES))This twoday workshop will consist of various talks given by prominent female mathematicians in the field. These will be appropriate for graduate students, postdocs, and researchers in areas related to the program. The workshop will also include a professional development session.
This workshop is open to all mathematicians.
Updated on Jun 12, 2018 09:17 AM PDT 
Program Mathematical problems in fluid dynamics
Organizers: Thomas Alazard (École Normale Supérieure; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Université ParisEst Créteil ValdeMarne; Centre National de la Recherche Scientifique (CNRS)), Mihaela Ifrim (University of WisconsinMadison), Igor Kukavica (University of Southern California), David Lannes (Université de Bordeaux I; Centre National de la Recherche Scientifique (CNRS)), LEAD Daniel Tataru (University of California, Berkeley)Fluid dynamics is one of the classical areas of partial differential equations, and has been the subject of extensive research over hundreds of years. It is perhaps one of the most challenging and exciting fields of scientific pursuit simply because of the complexity of the subject and the endless breadth of applications.
The focus of the program is on incompressible fluids, where water is a primary example. The fundamental equations in this area are the wellknown Euler equations for inviscid fluids, and the NavierStokes equations for the viscous fluids. Relating the two is the problem of the zero viscosity limit, and its connection to the phenomena of turbulence. Water waves, or more generally interface problems in fluids, represent another target area for the program. Both theoretical and numerical aspects will be considered.
Updated on Jan 24, 2018 10:14 AM PST
Past Scientific Events

Seminar Tutorial on Lyapunov functions and Isolating blocks.
Created on Dec 05, 2018 03:14 PM PST 
Seminar Arnold Diffusion
Created on Dec 05, 2018 03:17 PM PST 
Seminar Hamiltonian Seminar: Oscillatory orbits in the planar three body problem for all values of the masses
Updated on Nov 29, 2018 11:19 AM PST 
Seminar Graduate Student Seminar
Created on Sep 07, 2018 01:47 PM PDT 
Seminar Chancellor Course: Topics in Analysis
Updated on Aug 17, 2018 03:34 PM PDT 
Seminar Weak KAM Theory, Homogenization and Symplectic Topology
Created on Aug 24, 2018 03:42 PM PDT 
Seminar Celestial Mechanics: Variational construction of periodic and heteroclinic orbits in the planar Sitnikov problem
Updated on Nov 27, 2018 09:45 AM PST 
Seminar Lunch with Hamilton: Modeling the interaction of electromagnetic waves with beams and plasma using variational principles and Hamiltonian analysis
Updated on Nov 29, 2018 02:52 PM PST 
Seminar Chancellor Course: Topics in Analysis
Updated on Aug 17, 2018 03:33 PM PDT 
Seminar Weak KAM Theory, Homogenization and Symplectic Topology
Created on Aug 24, 2018 03:42 PM PDT 
Seminar Hamiltonian Colloquium: Dynamical zeta functions and topology for negatively curved surfaces
Updated on Nov 28, 2018 11:04 AM PST 
Seminar Chancellor Course: Topics in Analysis
Updated on Aug 17, 2018 03:33 PM PDT 
Seminar Weak KAM Theory, Homogenization and Symplectic Topology
Created on Aug 24, 2018 03:42 PM PDT 
Seminar Chancellor Course: Topics in Analysis
Updated on Aug 17, 2018 03:32 PM PDT 
Seminar Weak KAM Theory, Homogenization and Symplectic Topology
Created on Aug 24, 2018 03:42 PM PDT 
Workshop Hamiltonian systems, from topology to applications through analysis II
Organizers: Alessandra Celletti (Seconda Università di Roma "Tor Vergata''), Rafael de la Llave (Georgia Institute of Technology), Diego delCastilloNegrete (Oak Ridge National Laboratory), Lawrence Evans (University of California, Berkeley), LEAD Philip Morrison (University of Texas, Austin), Sergei Tabachnikov (Pennsylvania State University), Amie Wilkinson (University of Chicago)This is a main workshop of the program “Hamiltonian systems, from topology to applications through analysis.” It will feature current developments pertaining to finite and infinitedimensional Hamiltonian systems, with a mix of rigorous theory and applications. A broad range of topics will be included, e.g., existence of and transport about invariant sets (Arnold diffusion, KAM, etc.), techniques for projection/reduction of infinite to finite systems, and the role of topological invariants in applications.
Updated on Nov 30, 2018 10:40 AM PST 
Seminar Combinatorics Seminar: Cyclotomic factors of necklace polynomials.
Updated on Nov 15, 2018 11:30 AM PST 
Seminar Lunch with Hamilton: 3D Billiards: visualization of the 4D phase space and powerlaw trapping of chaotic trajectories
Created on Nov 15, 2018 09:09 AM PST 
Seminar Chancellor Course: Topics in Analysis
Updated on Aug 17, 2018 03:32 PM PDT 
Seminar Weak KAM Theory, Homogenization and Symplectic Topology
Created on Aug 24, 2018 03:42 PM PDT 
Seminar Combinatorics Seminar: Electrical networks and hyperplane arrangements
Updated on Nov 13, 2018 12:29 PM PST 
Seminar Hamiltonian Postdoc Workshop: Emphasizing nonlinear behaviors for cubic coupled systems
Updated on Nov 16, 2018 09:39 AM PST 
Seminar Hamiltonian Postdoc Workshop: The effect of threshold energy obstructions on the L 1 → L∞ dispersive esti mates for some Schr ̈odinger type equations
Updated on Nov 16, 2018 09:40 AM PST 
Seminar Hamiltonian Postdoc Workshop: Linear WhithamBoussinesq modes in channels of constant crosssection and trapped modes associated with continental shelves.
Updated on Nov 16, 2018 09:41 AM PST 
Seminar Hamiltonian Postdoc Workshop: Critical transition to the inverse cascade
Updated on Nov 16, 2018 09:43 AM PST 
Seminar Hamiltonian Seminar: Construction of unstable KAM tori for a system of coupled NLS equations.
Updated on Nov 16, 2018 08:43 AM PST